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The ratio of two numbers is 4:54:5 after adding 2020 to the smaller number and Subtracting 2020 from the greater number the ratio becomes 14:1314:13. Find the numbers.

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Full solution

Q. The ratio of two numbers is 4:54:5 after adding 2020 to the smaller number and Subtracting 2020 from the greater number the ratio becomes 14:1314:13. Find the numbers.
  1. Identify Ratio Equations: Identify the initial ratio and set up the equations using variables.\newlineLet the smaller number be 4x4x and the larger number be 5x5x.
  2. Set Up Equations: Apply the changes to the numbers and set up the second ratio equation.\newline(4x+20)/(5x−20)=1413(4x + 20) / (5x - 20) = \frac{14}{13}
  3. Cross-Multiply: Cross-multiply to solve for xx.13(4x+20)=14(5x−20)13(4x + 20) = 14(5x - 20)52x+260=70x−28052x + 260 = 70x - 280
  4. Solve for x: Simplify and solve for x.\newline70x−52x=260+28070x - 52x = 260 + 280\newline18x=54018x = 540\newlinex=30x = 30
  5. Substitute Back: Substitute xx back into the original numbers.\newlineSmaller number = 4x=4(30)=1204x = 4(30) = 120\newlineLarger number = 5x=5(30)=1505x = 5(30) = 150

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